简介：不精确的牛顿方法被把牛顿的方法与被用来不正确地解决牛顿方程的另一个反复的方法相结合构造。在这篇论文，我们为不精确的牛顿方法建立二条半本地人集中定理。当这二条定理被指定到牛顿的方法时，我们关于牛顿的方法获得一条不同Newton-Kantorovich定理。当为解决牛顿方程的反复的方法被指定是切开的方法时，我们为特殊不精确的牛顿方法关于重复步得到二估计。

简介：AconicNewtonmethodisattractivebecauseitconvergestoalocalminimizzerrapidlyfromanysufficientlygoodinitialguess.However,itmaybeexpensivetosolvetheconicNewtonequationateachiterate.InthispaperweconsideraninexactconicNewtonmethod,whichsolvesthecouicNewtonequationoldyapproximatelyandinsonmunspecifiedmanner.Furthermore,weshowthatsuchmethodislocallyconvergentandcharacterizestheorderofconvergenceintermsoftherateofconvergenceoftherelativeresiduals.

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简介：Thispaperrepresentsaninexactsequentialquadraticprogramming(SQP)algorithmwhichcansolvenonlinearprogramming(NLP)problems.Aninexactsolutionofthequadraticprogrammingsubproblemisdeterminedbyaprojectionandcontractionmethodsuchthatonlymatrix-vectorproductisrequired.SometruncatedcriteriaarechosensuchthatthealgorithmissuitabletolargescaleNLPproblem.Theglobalconvergenceofthealgorithmisproved.

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简介：Inthispaperweconsidertheglobalconvergenceofanyconjugategradientmethodoftheformd1=-g1,dk+1=-gk+1+βkdk(k≥1)withanyβksatisfyingsumeconditions,andwiththestrongwolfelinesearchconditions.Undertheconvexassumptionontheobjectivefunction,weprevethedescenfpropertyandtheglobalconvergenceofthismethod.

简介：Inthisstudy,weuseinexactnewtonmethodstofindsolutionsofnonlinear,nondifferenti-ableoperatorequationsonBanachspaceswithaconvergencestructure.ThistechniqueinvolvestheintroductionofageneralizednormasanoperatorfromalinearspaceintoapartiallyorderedBanachspace.Inthiswaythemetricpropertiesoftheexaminedproblemcanbeanalyzedmoreprecisely.Moreover,thisapproachallmvsustoderivefromthesametheorem,ontheonehand,semi-localresultsofKantorovich-type,andontheotherhand,globalresultsbasedonmono-tonicityconsiderations.Furthermore,iveshowthatspecialcasesofourresultsreducetothecorrespondingonesalreadyintheliterature.Finally>ourresultsareusedtosolveintegralequationsthatcannotbesolvedwithexistingmethods.

简介：EllipticPDE-constrainedoptimalcontrolproblemswithL^1-controlcost(L^1-EOCP)areconsidered.TosolveL^1-EOCP,theprimal-dualactiveset(PDAS)method,whichisaspecialsemismoothNewton(SSN)method,usedtobeapriority.However,ingeneralsolvingNewtonequationsisexpensive.Motivatedbythesuccessofalternatingdirectionmethodofmultipliers(ADMM),weconsiderextendingtheADMMtoL^1-EOCP.TodiscretizeL^1-EOCP,thepiecewiselinearfiniteelement(FE)isconsidered.However,differentfromthefinitedimensionalL^1-norm,thediscretizedL^1-normdoesnothaveadecoupledform.Toovercomethisdifficulty,aneffectiveapproachisutilizingnodalquadratureformulastoapproximatelydiscretizetheL^1-normandL^2-norm.Itisprovedthattheseapproximationstepswillnotchangetheorderoferrorestimates.Tosolvethediscretizedproblem,aninexactheterogeneousADMM(ihADMM)isproposed.DifferentfromtheclassicalADMM,theihADMMadoptstwodifferentweightedinnerproductstodefinetheaugmentedLagrangianfunctionintwosubproblems,respectively.Benefitingfromsuchdifferentweightedtechniques,twosubproblemsofihADMMcanbeefficientlyimplemented.Furthermore,theoreticalresultsontheglobalconvergenceaswellastheiterationcomplexityresultso(1/k)forihADMMaregiven.Inordertoobtainmoreaccuratesolution,atwo-phasestrategyisalsopresented,inwhichtheprimal-dualactiveset(PDAS)methodisusedasapostprocessoroftheihADMM.Numericalresultsnotonlyconfirmerrorestimates,butalsoshowthattheihADMMandthetwo-phasestrategyarehighlyefficient.